Iterative Solution of Nonlinear Equations of the F-Strongly Accretive Type

Let q)1, and let E be a real q-uniformly smooth Banach space. Let T: EªE be a Lipschitz f-strongly accretive operator and suppose the equation Txsf, fgE, has a solution. It is proved that under suitable conditions on the real sequences an4`ns0 and bn4`ns0, the iteration process x0gE yns 1ybn.xnqbn fq IyT.xn., nG0 xnq1s 1yan.xnqan fq IyT.yn., nG0 converges strongly to the unique solution of the equation Txsf. A related result deals with the approximation of fixed points of f-hemicontractive operators}a class of operators which is much more general than the important class of strongly pseudocontractive operators